A324660 Starting at n, a(n) is the total number of moves made to the right according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away from zero instead.

0, 0, 1, 0, 10, 11, 0, 861, 4, 5, 0, 11, 59, 60, 5, 0, 57, 390898, 7, 8, 66444, 0, 22, 11, 12, 610392, 8, 9, 0, 211, 4434560, 266001, 266000, 266001, 266002, 9, 0, 43, 106674, 106673, 120, 12, 11, 12, 495, 0, 67, 50, 51, 36, 37, 100, 25, 12, 13, 0, 317, 316

Offset

0,5

Links

Table of n, a(n) for n=0..57.

Example

For n=2, the points visited are 2,1,-1,-4,0 with the move from -4 to 0 being the only one to the right, hence a(2)=1.

Prog

(Python)
#Sequences A324660-A324692 generated by manipulating this trip function
#spots - positions in order with possible repetition
#flee - positions from which we move away from zero with possible repetition
#stuck - positions from which we move to a spot already visited with possible repetition
def trip(n):
    stucklist = list()
    spotsvisited = [n]
    leavingspots = list()
    turn = 0
    forbidden = {n}
    while n != 0:
        turn += 1
        sign = n // abs(n)
        st = sign * turn
        if n - st not in forbidden:
            n = n - st
        else:
            leavingspots.append(n)
            if n + st in forbidden:
                stucklist.append(n)
            n = n + st
        spotsvisited.append(n)
        forbidden.add(n)
    return {'stuck':stucklist, 'spots':spotsvisited,
                'turns':turn, 'flee':leavingspots}
#Actual sequence
def a(n):
    d=trip(n)
    return sum(1 for i in range(d['turns']) if d['spots'][i+1] > d['spots'][i])

Crossrefs

Cf. A228474, A324660-A324692

Sequence in context: A079793 A086884 A284201 * A336035 A334676 A176998

Adjacent sequences: A324657 A324658 A324659 * A324661 A324662 A324663

Keyword

nonn

Author

David Nacin, Mar 10 2019

Status

approved